Additive noise is one of the main challenges for automatic speaker recognition and several compensation techniques have been proposed to deal with this problem. In this paper, we present a new “data-driven” denoising technique operating in the i-vector space based on a joint modeling of clean and noisy i-vectors. The joint distribution is estimated using a large set of i-vectors pairs (clean i-vectors and their noisy versions generated artificially) then integrated in an MMSE estimator in the test phase to compute a “cleaned-up” version of noisy test i-vectors. We show that this algorithm achieves up to 80% of relative improvement in EER. We also present a version of the proposed algorithm that can be used to compensate multiple “unseen” noises. We test this technique on the recently published SITW database and show a significant gain compared to the baseline system performance.